Limitations:
Determining the number of samples needed to satisfy the assumption of Section , namely, the number of samples needed to guarantee the convergence rate provided in Theorem REF , is a long-standing open problem. There is work on this subject ranging from pure optimization [1]} to Importance Weighted Autoencoders [2]}. In this paper, our goal is to characterize the problem theoretically in terms of convergence rates. We believe that this clarifies the ongoing gap between theory and practice. Despite this gap, we found empirically that 100 Monte-Carlo samples was sufficient.
